Animate the attached SigmaHook logo created in this job (silver metallic coat hook at top, thin silver string hanging down, gold metallic ring with σ at bottom) as a smooth pendulum swing.

Motion: The entire assembly swings from the hook's tip as the pivot point. Natural pendulum physics — slow at the extremes, fast through the center.

Sequence (total ~4 seconds):

Starts at rest, centered, perfectly still (0.5s hold)

Swings right to ~8°, hangs briefly at the top, swings back through center

Swings left to ~8°, hangs briefly, swings back through center

Swings right to ~5°, hangs, swings back through center

Swings left to ~5°, hangs, swings back through center

Swings right to ~2°, swings back through center

Swings left to ~2°, swings back through center

Settles at center. Perfectly still. (0.5s hold)

Style: Smooth, continuous motion. No jerky stops. No bouncing. The pendulum decays naturally like a real object losing energy. The "hang" at each extreme is a brief deceleration, not a pause.

Output: 512×700px, 60fps. Frame 1 and last frame are identical (logo centered, at rest).

Background: Transparent (WebM with alpha channel) if possible. If transparent output is not supported, use solid black (#0A0C10) background instead.

The static logo image is attached. Animate only the rotation. Do not change the design, colors, or proportions.